Suppose each value of M has a standard deviation associated with it. What is the standard deviation of X? Is it a simpler calculation if the standard deviation of each M is the same?

This is from my wife's friend. It's been over 25 years since I've done statistics so I'm rusty and trying to brush up. Any help would be appreciated.

Oh...and the notation is the way it is because I've not figured out how to get series fonts to work.

Let me clarify:

1) You have a number of random variables M_1 .... M_n and you form the product R= (1+M_1)(1+M_2)...(1+M_n). Those M_i are real valued, independent, and are following an identical distribution.

2) Are asking whether there is a random variable X such that the product R equals (1+X)^n ?

Obviously if n is even and those M are following the Gaussian law then such an X doesn't exist - the right hand side is always positive, while the probability for the left hand to be negative is positive :-)

Dieb -

1) I confess I'm confused on this point as well, but your summary is my take as well.

2) No, I don't think so. I think the friend is asking what the standard deviation of X would be given a standard deviation of Mi. On top of that, she wants to know whether the calculation is easier if the standard deviation of Mi is the same throughout the series. Seems to me that the calculation has the exact same difficulty either way as "calculation difficulty" seems somewhat subjective once you are dealing with standard deviations, but perhaps she's asking whether the notation of the calculation requires more variables if the standard deviation of Mi is not the same.

Your note on the Gaussian law gave me a chuckle. I don't think that my wife's friend was thinking in terms of physics when she posted the problem (but then, I don't actually know that) and I doubt it applies to any inverse square type calculation, but then that's a bit out of my area of knowledge anyway. I'm tempted to note the X likely can't exist for that reason though just to see her response. :-)

If this is a textbook exercise I'd assume that all the M_i are Bernoulli experiments and that the reference to ''standard deviation'' was misleading. In this case, the product equals 2^X, where X is following a binomial distribution B(n,p).

If this is a textbook exercise I'd assume that all the M_i are Bernoulli experiments and that the reference to ''standard deviation'' was misleading. In this case, the product equals 2^X, where X is following a binomial distribution B(n,p).

My assumption is that the equation is a straight up statistics problem, but again I'm so rusty that I'm having a tough time trying to solve it. I'm not sure that the variables are supposed to be assumed to be binary, but if so, I have no idea what my friend's question regarding different deviations across Mi would mean. Very confusing.

--------------we IDists rule in design for the flagellum and cilium largely because they do look designed. Bilbo

The only reason you reject Thor is because, like a cushion, you bear the imprint of the biggest arse that sat on you. Louis

I don't claim to be pure, and we've certainly ragged on poor O'Leary, but geez. Where all the sciency supermodels be at?

Any social gathering has its share of sexual energy, but grabbity is just juvenile and rude. You gotta wonder what if anything is going through these guys' minds. What do they think is gonna happen?

I often feel guilty about reacting -- even only silently, internally -- to a woman's looks/wit/vitality. I'm still listening to what she's saying but all I can think is holy crap what beautiful eyes/hair/voice w.h.y.

I have a couple of very attractive blonde friends who've dyed their hair and cut it off or tied it back because they've felt they weren't being taken seriously.

:-(

"Is a puzzlement."

But always remember that people who get bothered about so-called "sexual harrassment" and alleged "misogynistic behavior" are, at absolute best, making mountains out of molehills, because there aren't hardly any women who genuinely are on the short end of that kind of stuff. Isn't that right, S-dog?

Did I ever say anything like that, or did you swallow the FTB/A+ Koolaid?

Just asking...

--------------"Hail is made out of water? Are you really that stupid?" Joe G

"I have a better suggestion, Kris. How about a game of hide and go fuck yourself instead." Louis

"The reason people use a crucifix against vampires is that vampires are allergic to bullshit" Richard Pryor

I don't claim to be pure, and we've certainly ragged on poor O'Leary, but geez. Where all the sciency supermodels be at?

Any social gathering has its share of sexual energy, but grabbity is just juvenile and rude. You gotta wonder what if anything is going through these guys' minds. What do they think is gonna happen?

I often feel guilty about reacting -- even only silently, internally -- to a woman's looks/wit/vitality. I'm still listening to what she's saying but all I can think is holy crap what beautiful eyes/hair/voice w.h.y.

I have a couple of very attractive blonde friends who've dyed their hair and cut it off or tied it back because they've felt they weren't being taken seriously.

:-(

"Is a puzzlement."

But always remember that people who get bothered about so-called "sexual harrassment" and alleged "misogynistic behavior" are, at absolute best, making mountains out of molehills, because there aren't hardly any women who genuinely are on the short end of that kind of stuff. Isn't that right, S-dog?

Did I ever say anything like that, or did you swallow the FTB/A+ Koolaid?

Just asking...

The seemingly complete inability of the FTB/A+theism crowd to accurately represent differing viewpoints reminds me strongly of the creationists at UD. While I'm tempted to chalk it up to deliberate straw-manning, I try to give them the benefit of the doubt and assume they're just stupid. So less like Dembski, more like JoeG.

--------------Lou FCD is still in school, so we should only count him as a baby biologist. -carlsonjok -deprecatedI think I might love you. Don't tell Deadman -Wolfhound

--------------"But it's disturbing to think someone actually thinks creationism -- having put it's hand on the hot stove every day for the last 400 years -- will get a different result tomorrow." -- midwifetoad

I don't claim to be pure, and we've certainly ragged on poor O'Leary, but geez. Where all the sciency supermodels be at?

Any social gathering has its share of sexual energy, but grabbity is just juvenile and rude. You gotta wonder what if anything is going through these guys' minds. What do they think is gonna happen?

I often feel guilty about reacting -- even only silently, internally -- to a woman's looks/wit/vitality. I'm still listening to what she's saying but all I can think is holy crap what beautiful eyes/hair/voice w.h.y.

I have a couple of very attractive blonde friends who've dyed their hair and cut it off or tied it back because they've felt they weren't being taken seriously.

:-(

"Is a puzzlement."

But always remember that people who get bothered about so-called "sexual harrassment" and alleged "misogynistic behavior" are, at absolute best, making mountains out of molehills, because there aren't hardly any women who genuinely are on the short end of that kind of stuff. Isn't that right, S-dog?

Did I ever say anything like that, or did you swallow the FTB/A+ Koolaid?

Just asking...

Consider your chain yanked, P.

--------------"But it's disturbing to think someone actually thinks creationism -- having put it's hand on the hot stove every day for the last 400 years -- will get a different result tomorrow." -- midwifetoad

The seemingly complete inability of the FTB/A+theism crowd to accurately represent differing viewpoints reminds me strongly of the creationists at UD. While I'm tempted to chalk it up to deliberate straw-manning, I try to give them the benefit of the doubt and assume they're just stupid. So less like Dembski, more like JoeG.

Aye, there's the rub.

Somewhere out there is a reasonable discussion about the differences between individual sexual behaviour and gender bigotry.

Haven't seen it, myself, but it must be out there somewhere...

--------------"But it's disturbing to think someone actually thinks creationism -- having put it's hand on the hot stove every day for the last 400 years -- will get a different result tomorrow." -- midwifetoad

The seemingly complete inability of the FTB/A+theism crowd to accurately represent differing viewpoints reminds me strongly of the creationists at UD. While I'm tempted to chalk it up to deliberate straw-manning, I try to give them the benefit of the doubt and assume they're just stupid. So less like Dembski, more like JoeG.

Aye, there's the rub.

Somewhere out there is a reasonable discussion about the differences between individual sexual behaviour and gender bigotry.

Haven't seen it, myself, but it must be out there somewhere...

It would be an interesting discussion, so if you find it, please do let me know.

--------------Lou FCD is still in school, so we should only count him as a baby biologist. -carlsonjok -deprecatedI think I might love you. Don't tell Deadman -Wolfhound

If this is a textbook exercise I'd assume that all the M_i are Bernoulli experiments and that the reference to ''standard deviation'' was misleading. In this case, the product equals 2^X, where X is following a binomial distribution B(n,p).

My assumption is that the equation is a straight up statistics problem, but again I'm so rusty that I'm having a tough time trying to solve it. I'm not sure that the variables are supposed to be assumed to be binary, but if so, I have no idea what my friend's question regarding different deviations across Mi would mean. Very confusing.

It doesn't look like a standard problem. The pdf is horrible, because it involves multiple products. There's probably a reasonable approximation if you expand the brackets and apply a central limit theorem to each term, but the devil's in the detail.

If each M_i follows a Cauchy distribution I'll pay to watch you solve it.

--------------It is fun to dip into the various threads to watch cluelessness at work in the hands of the confident exponent. - Soapy Sam (so say we all)

The seemingly complete inability of the FTB/A+theism crowd to accurately represent differing viewpoints reminds me strongly of the creationists at UD. While I'm tempted to chalk it up to deliberate straw-manning, I try to give them the benefit of the doubt and assume they're just stupid. So less like Dembski, more like JoeG.

Aye, there's the rub.

Somewhere out there is a reasonable discussion about the differences between individual sexual behaviour and gender bigotry.

Haven't seen it, myself, but it must be out there somewhere...

It would be an interesting discussion, so if you find it, please do let me know.

There's a very well behaved discussion at SkepticInk... not really gender discrimination and sexual behavior... but I'm sure they could come up with something.

In fact, if you want to write something up, even with just questions, I'll be happy to post it for you.

--------------Ignored by those who can't provide evidence for their claims.

It doesn't look like a standard problem. The pdf is horrible, because it involves multiple products. There's probably a reasonable approximation if you expand the brackets and apply a central limit theorem to each term, but the devil's in the detail.

If each M_i follows a Cauchy distribution I'll pay to watch you solve it.

Thanks Bob! Alas, no answer thus far.

--------------we IDists rule in design for the flagellum and cilium largely because they do look designed. Bilbo

The only reason you reject Thor is because, like a cushion, you bear the imprint of the biggest arse that sat on you. Louis

OK i know we aren't supposed to fight about talk club but i just love this tard sooo much that i must share it with you guys because i love you too

this idiot Chad Elliott is seriously a god-tier tard. you will look the entire internet over and not find a bigger fucking moron in any tube. the depth of this man's stupidity is staggering. the style in which he plays prometheus answering voltaire's prayer, daily, it would be a shame if i were to try to describe it without you reading it for yourself.

Now listen this is a pet but i don't feed him. you don't have to. there is a constant stream of neckbearded gnu athiest autistic types facebooking and youtubing him to death. for fuck's sake don't do that. just watch, and enjoy, for he does this shit for free.

The background is that my SF club has a science discussion board that is regularly tarded up by a John Birch Society, precious bodily fluids-level reactionary dude who is very anti-realist in many ways, but especially so on GW. We jousted back and forth every time he posted his shit, but everyone else got sick and tired of it, so the organizer asked us to write one essay each and leave it at that. This is mine. No idea if the other guy will man up and write something.

--------------"But it's disturbing to think someone actually thinks creationism -- having put it's hand on the hot stove every day for the last 400 years -- will get a different result tomorrow." -- midwifetoad

I am about to win a steak dinner in a few hrs. There's a Faux News head at work who thinks I'm a sucker because everybody knows Obama is an incompetent failure who is about to lose to the real american job creator in a momentous landslide. He eagerly took my bet, and last week, tried to up it to include dinner for the missus.

I am about to win a steak dinner in a few hrs. There's a Faux News head at work who thinks I'm a sucker because everybody knows Obama is an incompetent failure who is about to lose to the real american job creator in a momentous landslide. He eagerly took my bet, and last week, tried to up it to include dinner for the missus.

Don't forget to take his guns and make him marry a man.

--------------Math is just a language of reality. Its a waste of time to know it. - Robert Byers

I am about to win a steak dinner in a few hrs. There's a Faux News head at work who thinks I'm a sucker because everybody knows Obama is an incompetent failure who is about to lose to the real american job creator in a momentous landslide. He eagerly took my bet, and last week, tried to up it to include dinner for the missus.